Ideals generated by submaximal minors - Mathematics > Algebraic GeometryReport as inadecuate

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Abstract: The goal of this paper is to study irreducible families Wb;a of codimension4, arithmetically Gorenstein schemes X of P^n defined by the submaximal minorsof a t x t matrix A with entries homogeneous forms of degree a j-b i. Undersome numerical assumption on a j and b i we prove that the closure of Wb;a isan irreducible component of Hilb^{px}P^n, we show that Hilb^{px}P^n isgenerically smooth along Wb;a and we compute the dimension of Wb;a in termsof a j and b i. To achieve these results we first prove that X is determined bya regular section of the twisted conormal sheaf I Y-I^2 Ys wheres=degdetA and Y is a codimension 2, arithmetically Cohen-Macaulay scheme ofP^n defined by the maximal minors of the matrix obtained deleting a suitablerow of A.

Author: Jan O. Kleppe, Rosa M. Miro-Roig


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